$(20$ points$)$ Question $2$: $($User defined function$)$

A rocket is launched vertically. At time the rocket's engine shuts down. At that time, the rocket has reached an altitude of $500m$ and is rising at a velocity of $125\frac{m}{s}.$ Gravity then takes over. The height of the rocket as a function of time is

$h(t)=-\frac{9\mathrm{.}8}{2}{t}^2+125t+500$ for $t>0$

$($a$)$Create a function named 'Calcheight' that accepts time as an input and returns the height of the rocket. Use your function in your solutions to parts b and $c.$

$($b$)$Plot height vs$.$ time for times from $0$ to $60$ seconds. Use an increment of $2$ second in your time vector.

$($c$)$ Find the time when the rocket will hit to the ground.

Disclaimer: Solve the code using the knowledge you learned $($Use If$,$ Else$-$if and display command. 'for loop' cannot be used in your code$)$ in class without relying on AI tools.